There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ \frac{{x}^{3}}{(6(1 - x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(-6x + 6)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(-6x + 6)}\right)}{dx}\\=&(\frac{-(-6 + 0)}{(-6x + 6)^{2}})x^{3} + \frac{3x^{2}}{(-6x + 6)}\\=&\frac{6x^{3}}{(-6x + 6)^{2}} + \frac{3x^{2}}{(-6x + 6)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{6x^{3}}{(-6x + 6)^{2}} + \frac{3x^{2}}{(-6x + 6)}\right)}{dx}\\=&6(\frac{-2(-6 + 0)}{(-6x + 6)^{3}})x^{3} + \frac{6*3x^{2}}{(-6x + 6)^{2}} + 3(\frac{-(-6 + 0)}{(-6x + 6)^{2}})x^{2} + \frac{3*2x}{(-6x + 6)}\\=&\frac{72x^{3}}{(-6x + 6)^{3}} + \frac{36x^{2}}{(-6x + 6)^{2}} + \frac{6x}{(-6x + 6)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{72x^{3}}{(-6x + 6)^{3}} + \frac{36x^{2}}{(-6x + 6)^{2}} + \frac{6x}{(-6x + 6)}\right)}{dx}\\=&72(\frac{-3(-6 + 0)}{(-6x + 6)^{4}})x^{3} + \frac{72*3x^{2}}{(-6x + 6)^{3}} + 36(\frac{-2(-6 + 0)}{(-6x + 6)^{3}})x^{2} + \frac{36*2x}{(-6x + 6)^{2}} + 6(\frac{-(-6 + 0)}{(-6x + 6)^{2}})x + \frac{6}{(-6x + 6)}\\=&\frac{1296x^{3}}{(-6x + 6)^{4}} + \frac{648x^{2}}{(-6x + 6)^{3}} + \frac{108x}{(-6x + 6)^{2}} + \frac{6}{(-6x + 6)}\\ \end{split}\end{equation} \]

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